There are two main types of AAR -- well, and a third type, I guess, which is a combination of the first two.
One type is 'novel-like' with characters experiencing the events in question, and telling us their thoughts and feelings about it. For example:
'Commander Nelson reclined in her acceleration couch, as the countdown clicked through the final seconds. With a roar the jets of atomized Sorium fuel snapped on and the TFNS Swiftsure left Earth orbit for humanity's first journey to another star.'
The other type is 'encyclopedia-like' where the "facts" of the events are recounted. For example:
'The empire's first jump-capable ship, TFNS Swiftsure under C.O. Commander Nelson, is sent to probe the closest wormhole.'
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I highly recommend the second version. It requires less skill to write an interesting recap of events than it does to write good fiction.
My other advice is to not drown the reader in trivia. While I want to know what ships were launched or what new technologies were discovered this year, I don't need a day-by-day breakdown, or a long list of calendar dates & launchings & discoveries. It's hard to pin down the right amount of detail, but personally I don't want to read long tables of info. It's fine to say ". . .and fifteen other asteroids with a half-dozen automines each."
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Oh, and my number one piece of advice is don't use the same names as everyone else. I literally can't count the number of Battles of Sigma Draconis or Wolf something-something-something aliens or Gliese number-number-number colonies I've read about. I can't count them, because I can't keep them straight. If you must set your game on Earth, try to rename the other solar colonies, if not the bodies themselves. Your AAR will be much more memorable if it features "Tycho City" instead of "Luna" or "Uj Debreczen" instead of "Mars."